Chen Dali, Wu Yuwei, Li Jingquan, Ding Xiaohui, Chen Caihua
School of Management and Engineering, Nanjing University, Nanjing, 210093 China.
Department of Mathematics, National University of Singapore, Singapore, 117576 Singapore.
J Glob Optim. 2022 May 16:1-23. doi: 10.1007/s10898-022-01171-x.
Data uncertainty has a great impact on portfolio selection. Based on the popular mean-absolute deviation (MAD) model, we investigate how to make robust portfolio decisions. In this paper, a novel Wasserstein metric-based data-driven distributionally robust mean-absolute deviation (DR-MAD) model is proposed. However, the proposed model is non-convex with an infinite-dimensional inner problem. To solve this model, we prove that it can be transformed into two simple finite-dimensional linear programs. Consequently, the problem can be solved as easily as solving the classic MAD model. Furthermore, the proposed DR-MAD model is compared with the 1/N, classic MAD and mean-variance model on S &P 500 constituent stocks in six different settings. The experimental results show that the portfolios constructed by DR-MAD model are superior to the benchmarks in terms of profitability and stability in most fluctuating markets. This result suggests that Wasserstein distributionally robust optimization framework is an effective approach to address data uncertainty in portfolio optimization.
数据不确定性对投资组合选择有很大影响。基于流行的平均绝对偏差（MAD）模型，我们研究如何做出稳健的投资组合决策。本文提出了一种基于Wasserstein度量的新型数据驱动的分布鲁棒平均绝对偏差（DR-MAD）模型。然而，所提出的模型是非凸的，且存在无限维的内部问题。为了解决这个模型，我们证明它可以转化为两个简单的有限维线性规划。因此，该问题可以像求解经典MAD模型一样轻松解决。此外，在六种不同情况下，将所提出的DR-MAD模型与1/N、经典MAD和均值-方差模型在标准普尔500指数成分股上进行了比较。实验结果表明，在大多数波动市场中，由DR-MAD模型构建的投资组合在盈利能力和稳定性方面优于基准。这一结果表明，Wasserstein分布鲁棒优化框架是解决投资组合优化中数据不确定性的有效方法。
